onion_layers#

onion_layers(G)[source]#

Returns the layer of each vertex in an onion decomposition of the graph.

The onion decomposition refines the k-core decomposition by providing information on the internal organization of each k-shell. It is usually used alongside the core numbers.

Parameters:

GNetworkX graph: An undirected graph without self loops.

Returns:

od_layersdictionary: A dictionary keyed by node to the onion layer. The layers are contiguous integers starting at 1.

Raises:

NetworkXNotImplemented: If G is a multigraph or directed graph or if it contains self loops.

See also

core_number

References

[1]

Multi-scale structure and topological anomaly detection via a new network statistic: The onion decomposition L. Hébert-Dufresne, J. A. Grochow, and A. Allard Scientific Reports 6, 31708 (2016) http://doi.org/10.1038/srep31708

[2]

Percolation and the effective structure of complex networks A. Allard and L. Hébert-Dufresne Physical Review X 9, 011023 (2019) http://doi.org/10.1103/PhysRevX.9.011023

Examples

>>> degrees = [0, 1, 2, 2, 2, 2, 3]
>>> H = nx.havel_hakimi_graph(degrees)
>>> H.degree
DegreeView({0: 1, 1: 2, 2: 2, 3: 2, 4: 2, 5: 3, 6: 0})
>>> nx.onion_layers(H)
{6: 1, 0: 2, 4: 3, 1: 4, 2: 4, 3: 4, 5: 4}